When an object moves with respect to a reference frame, knowledge of the object's orientation with respect to the reference frame can be useful for deriving a variety of its parameters of motion. In fact, the orientation of an object with respect to a reference is usually required for navigating the object or obtaining information about its trajectory. Over time, many useful coordinate systems and methods have been developed to parameterize the equations of motion of such objects. For a theoretical background the reader is referred to textbooks on classical mechanics such as Goldstein et al., Classical Mechanics, 3rd Edition (Addison Wesley, 2002). For general examples of object tracking and orientation measurements a few examples can be found in U.S. Pat. No. 5,786,804 to Gordon and U.S. Pat. No. 6,023,291 to Kamel et al. as well as the references cited therein.
In one specific field of navigation it is important to know the inclination angle of an elongate object while it is in contact with a plane surface. Usually, inclination is defined as the angle between a line normal to the plane surface and an axis of the object that passes through its point of contact with the plane surface. In some cases, this axis is also the centerline of the elongate object. Various types of elongate objects can benefit from knowledge of their inclination while in contact with a plane surface. These objects include walking canes when in contact with the ground, pointers when in contact with a display or projection surface, writing devices when in contact with a writing surface, and styluses when in contact with an input screen.
In the field of input devices such as pens and styluses, inclination information is useful in order to analyze the information written or traced by the user. In principle, many methods can be adapted to measure pen inclination. Such methods can employ ranging devices using ultrasound, electromagnetic radiation including visible light and other apparatus. For example, U.S. Pat. No. 5,166,668 teaches a 3-axis detection method, U.S. Pat. No. 5,977,958 teaches a method using a difference in the time-of-flight of an electromagnetic wave, and still other references teach to apply the time-of-flight method to microwaves. Still other approaches use calibration marks, e.g., as described in U.S. Pat. Appl. 2003/0025951 or entire auxiliary calibration systems as described in U.S. Pat. Appl. 2002/0141616. Still another method for measuring the inclination of a pen employs sensors mounted in the pen for measuring magnetic fields created by magnetic dipoles oriented perpendicular to a writing board as described in U.S. Pat. Appl. 2002/0180714. Unfortunately, all of these methods are cumbersome and limiting to the user because the signals sent from the pen have to be received by external devices. In other words, the pen cannot independently determine its inclination with on-board equipment.
In principle, a pen equipped with inertial sensors such as gyroscopes and accelerometers can derive its inclination without dependence upon external devices. Japan patent application 6-67,799 proposes a method for determining the inclination angle by integrating the angular velocity of the pen obtained from a two-axis acceleration sensor. Also of interest are U.S. Pat. Nos. 5,902,968 and 5,981,884 using a three-axis acceleration sensor and a three-axis gyroscope. U.S. Pat. No. 5,434,371 teaches a structure in which an acceleration sensor is attached to the tip of a pen such to thus compensate the error due to pen inclination and a signal processing portion is located at the upper portion of the pen.
Unfortunately, inertial sensors suffer from drift errors and accumulation errors that typically increase quadratically with time for accelerometers and linearly with time for gyroscopes. To overcome these limitations of inertial sensors U.S. Pat. Appl. No. 2002/0148655 to Cho et al. teaches the use of an optical three-dimensional detecting device for detecting orientation angles of a centerline of an electronic pen relative to a ground and a height of the pen over a writing surface. Meanwhile, a three-axis accelerometer is used for detecting movement of the pen. The optical device has a portion such as a light source for radiating a beam to the writing surface to form beam spots and a detecting portion such as a camera and corresponding optics for detecting the beam spots from the light reflected off the writing surface.
Although Cho's teaching goes far to solve the problems, it still lacks the versatility, efficiency and accuracy to be employed in determining orientation parameters of writing devices and elongate objects in general.